Nonconforming rotated Q(1) element for Reissner-Mindlin plate

A new locking-free low order nonconforming rectangular finite element for t he Reissner-Mindlin plate is presented. It consists of the nonconforming ro tated Q(1) element for one of the rotation components and the conforming Q( 1) element for the other component together with the conforming Q(1) for th e deflection. This element gives optimal error bounds for all variables uni form in the plate thickness t with respect to the energy norm as well as th e L-2-norm. Moreover, we have derived another nonconforming rectangular ele ment with optimal error bounds uniform in t provided t = O(h).